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Popular Calculus Problems

d/(ds)((1-s^2)/((s^2+1)^2))	\frac{d}{ds}(\frac{1-s^{2}}{(s^{2}+1)^{2}})
integral of 1/(3(x-2))	\int\:\frac{1}{3(x-2)}dx
x^{''}+2x^'+x=0,x(0)=2,x^'(0)=1	x^{\prime\:\prime\:}+2x^{\prime\:}+x=0,x(0)=2,x^{\prime\:}(0)=1
(\partial)/(\partial y)(sqrt(4-y^2))	\frac{\partial\:}{\partial\:y}(\sqrt{4-y^{2}})
laplacetransform sin(t)sin(3t)	laplacetransform\:\sin(t)\sin(3t)
integral of cos^2(x/4)	\int\:\cos^{2}(\frac{x}{4})dx
integral of 1/(sqrt(x+9))	\int\:\frac{1}{\sqrt{x+9}}dx
integral of 4/(x^2+5x-14)	\int\:\frac{4}{x^{2}+5x-14}dx
integral of ln(14x)	\int\:\ln(14x)dx
limit as x approaches 1 of cos(pix)	\lim\:_{x\to\:1}(\cos(πx))
integral of (cos(2x))/(sin(2x))	\int\:\frac{\cos(2x)}{\sin(2x)}dx
limit as x approaches 8 of (x^2)/4-2/x	\lim\:_{x\to\:8}(\frac{x^{2}}{4}-\frac{2}{x})
derivative of (x^2+4x+3/(sqrt(x)))	\frac{d}{dx}(\frac{x^{2}+4x+3}{\sqrt{x}})
derivative of x-bln(x)	\frac{d}{dx}(x-b\ln(x))
inverse oflaplace (3s+7)/(s^2+4s+3)	inverselaplace\:\frac{3s+7}{s^{2}+4s+3}
derivative of {f}(xx)	\frac{d}{dx}({f}(x)x)
derivative of (2x+8x^2/((1+8x)^2))	\frac{d}{dx}(\frac{2x+8x^{2}}{(1+8x)^{2}})
sum from n=1 to infinity of (5n)/(4n+3)	\sum\:_{n=1}^{\infty\:}\frac{5n}{4n+3}
limit as h approaches 3 of ((-3h+5-5))/h	\lim\:_{h\to\:3}(\frac{(-3h+5-5)}{h})
limit as x approaches 3+of ln(x-3)	\lim\:_{x\to\:3+}(\ln(x-3))
limit as x approaches-3 of x-3	\lim\:_{x\to\:-3}(x-3)
f(x)=e(x^2+1)/2	f(x)=e\frac{x^{2}+1}{2}
derivative of (x^4)/(3-x^3)	derivative\:\frac{x^{4}}{3-x^{3}}
derivative of f(x)=arcsin(x^2)	derivative\:f(x)=\arcsin(x^{2})
derivative of (5x-3/(4x-3/x))	\frac{d}{dx}(\frac{5x-3}{4x-\frac{3}{x}})
integral of (2x+3)	\int\:(2x+3)dx
(\partial)/(\partial x)(xy^2+2x^2z)	\frac{\partial\:}{\partial\:x}(xy^{2}+2x^{2}z)
integral of cos(x)+sin(x)	\int\:\cos(x)+\sin(x)dx
integral of (x^4-5x^3+7x)/x	\int\:\frac{x^{4}-5x^{3}+7x}{x}dx
limit as x approaches 6 of (g(x))/(f(x))	\lim\:_{x\to\:6}(\frac{g(x)}{f(x)})
integral of (cos^2(x))/(sin^2(x))	\int\:\frac{\cos^{2}(x)}{\sin^{2}(x)}dx
derivative of 7x^2-5x+3	\frac{d}{dx}(7x^{2}-5x+3)
derivative of ((3e^{3x}))/3	derivative\:\frac{(3e^{3x})}{3}
integral of 1/(x^2-5x+4)	\int\:\frac{1}{x^{2}-5x+4}dx
integral of xsqrt(x^4)	\int\:x\sqrt{x^{4}}dx
y^'+5y=t+e^{-3t}	y^{\prime\:}+5y=t+e^{-3t}
integral of (x^3)/8	\int\:\frac{x^{3}}{8}dx
extreme f(x)=e^{rx}	extreme\:f(x)=e^{rx}
derivative of (x^6)/(x^2)	derivative\:\frac{x^{6}}{x^{2}}
tangent of f(x)=5+4x^2-2x^3,(2,5)	tangent\:f(x)=5+4x^{2}-2x^{3},(2,5)
integral of 1/(sqrt(30-x^2))	\int\:\frac{1}{\sqrt{30-x^{2}}}dx
integral of cos^5((3x)/2)sin^7((3x)/2)	\int\:\cos^{5}(\frac{3x}{2})\sin^{7}(\frac{3x}{2})dx
integral of-6sin(2x)+3cos(3x)	\int\:-6\cdot\:\sin(2x)+3\cdot\:\cos(3x)dx
derivative of \sqrt[3]{{g}(x})	\frac{d}{dx}(\sqrt[3]{{g}(x)})
derivative of sin^9(cos(8x))	\frac{d}{dx}(\sin^{9}(\cos(8x)))
integral of (8x+15)ln(2x)	\int\:(8x+15)\ln(2x)dx
integral of t^2e^{-9t}	\int\:t^{2}e^{-9t}dt
integral from 1 to 4 of (3ln(x))/(x^2)	\int\:_{1}^{4}\frac{3\ln(x)}{x^{2}}dx
derivative of (x^4/9)	\frac{d}{dx}(\frac{x^{4}}{9})
area y=2916sqrt(x),108x^2	area\:y=2916\sqrt{x},108x^{2}
integral of (x(2x-9))/(x^3-6x^2+12x-8)	\int\:\frac{x(2x-9)}{x^{3}-6x^{2}+12x-8}dx
integral of 7xe^{3x-1}	\int\:7xe^{3x-1}dx
(\partial)/(\partial x)(cos(y+x))	\frac{\partial\:}{\partial\:x}(\cos(y+x))
tangent of ((x+1)/(x-3))^2	tangent\:(\frac{x+1}{x-3})^{2}
integral from 0 to infinity of xe^{-x/a}	\int\:_{0}^{\infty\:}xe^{-\frac{x}{a}}dx
integral from 0 to N of e^{(-st)}sin(3t)	\int\:_{0}^{N}e^{(-st)}\sin(3t)dt
integral of 1/(7x+8)	\int\:\frac{1}{7x+8}dx
derivative of (0.1x^2-4.2x+6.5)^{1.5}	derivative\:(0.1x^{2}-4.2x+6.5)^{1.5}
derivative of e^{sec(8x)}	derivative\:e^{\sec(8x)}
sum from n=1 to infinity of 5/(2n^2+1)	\sum\:_{n=1}^{\infty\:}\frac{5}{2n^{2}+1}
integral of 1/1 (2x)	\int\:\frac{1}{1}(2x)dx
(\partial)/(\partial x)(x^2-2y^2+4)	\frac{\partial\:}{\partial\:x}(x^{2}-2y^{2}+4)
integral of 4x^3e^x	\int\:4x^{3}e^{x}dx
area 1/x ,0,y=1,y=e	area\:\frac{1}{x},0,y=1,y=e
limit as x approaches 3 of sqrt(x^3+6x)	\lim\:_{x\to\:3}(\sqrt{x^{3}+6x})
integral of (x-4)/(x^2+5x+6)	\int\:\frac{x-4}{x^{2}+5x+6}dx
derivative of y=((cos(x))/(1-sin(x)))^2	derivative\:y=(\frac{\cos(x)}{1-\sin(x)})^{2}
sum from n=1 to infinity of 1/(3^n+n^3)	\sum\:_{n=1}^{\infty\:}\frac{1}{3^{n}+n^{3}}
integral of t^{-2}e^t	\int\:t^{-2}e^{t}dt
slope of (-5,2),(5,-4)	slope\:(-5,2),(5,-4)
(dy)/(dx)-x/y =2y	\frac{dy}{dx}-\frac{x}{y}=2y
derivative of ln(1+4^x)	derivative\:\ln(1+4^{x})
(dy)/(dx)=x^7-1/(x^7)	\frac{dy}{dx}=x^{7}-\frac{1}{x^{7}}
derivative of sqrt(3+4x^2+9x^4)	\frac{d}{dx}(\sqrt{3+4x^{2}+9x^{4}})
integral from 0 to 1 of 2pix(2e^{-x^2})	\int\:_{0}^{1}2πx(2e^{-x^{2}})dx
integral from 0 to pi of tcos(2t)	\int\:_{0}^{π}t\cos(2t)dt
integral of ((x-2)(x+3))/(xsqrt(x))	\int\:\frac{(x-2)(x+3)}{x\sqrt{x}}dx
integral of ln(x^7)	\int\:\ln(x^{7})dx
(e^x+e^{-x})(dy)/(dx)=y^2	(e^{x}+e^{-x})\frac{dy}{dx}=y^{2}
integral of (2ax+b)(ax^2+bx)^7	\int\:(2ax+b)(ax^{2}+bx)^{7}dx
integral of e^{-3x}sin(2x)	\int\:e^{-3x}\sin(2x)dx
derivative of x^25^x	derivative\:x^{2}5^{x}
(\partial)/(\partial x)(ln(8x^2+y^2+3))	\frac{\partial\:}{\partial\:x}(\ln(8x^{2}+y^{2}+3))
(\partial)/(\partial y)(15x^2-9xy+25y^2)	\frac{\partial\:}{\partial\:y}(15x^{2}-9xy+25y^{2})
derivative of p(t)=12te^{-t/6}	derivative\:p(t)=12te^{-\frac{t}{6}}
integral of (x+1)/(x^4-4x^2)	\int\:\frac{x+1}{x^{4}-4x^{2}}dx
integral of ((y^2)/2-ytan(x))	\int\:(\frac{y^{2}}{2}-y\tan(x))dx
inverse oflaplace 9/(s(s^2+9s+9))	inverselaplace\:\frac{9}{s(s^{2}+9s+9)}
tangent of y=(1+2x)^2,\at x=1	tangent\:y=(1+2x)^{2},\at\:x=1
integral of 1/(sqrt(-3x^2+3x+7))	\int\:\frac{1}{\sqrt{-3x^{2}+3x+7}}dx
limit as x approaches 2 of 1/(2(x-2))	\lim\:_{x\to\:2}(\frac{1}{2(x-2)})
integral of 1/(sqrt(5-4x-x^2))	\int\:\frac{1}{\sqrt{5-4x-x^{2}}}dx
integral of cos(4x)	\int\:\cos(4x)dx
integral of ((x+1))/(x^2-4x+12)	\int\:\frac{(x+1)}{x^{2}-4x+12}dx
derivative of f(x)=cos(3x)	derivative\:f(x)=\cos(3x)
derivative of 3+2sin(x)	\frac{d}{dx}(3+2\sin(x))
integral from 0 to x of sqrt(a^2-x^2)	\int\:_{0}^{x}\sqrt{a^{2}-x^{2}}dx
derivative of y^2-x^3+8	\frac{d}{dx}(y^{2}-x^{3}+8)
taylor ln(x+1)	taylor\:\ln(x+1)
X^'	X^{\prime\:}

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